I too am having this problem. I have the breakout board from Adafruit for the DS1307. After setting the time with a Raspberry Pi I use it with a Trinket 5v. It keeps perfect time for a good long while, and then stops incrementing. My code recalculate's the display every time it gets a reading, and it keeps repeating the same time. When I hook it back up to the Raspberry Pi (before setting the time again), it starts incrementing again from the time that it was stuck on.